Assuming you're not going to have them authenticate with Facebook, LinkedIn or Open ID so what I would do is create additional fields in the User Settings that are simple text fields for both Facebook and Twitter. Let them simply copy and paste their profile link in it.
In the alternate form for the user, add those 2 new fields to the profile form and they should show for them to edit.
The Facebook, LinkedIn and Open IDs are for authentication from those providers not storing profile information. I'd not remove them as there is code written around them for authentication using those providers.